Quiz on Principal Component Analysis (PCA)

Principal Component Analysis Overview Answers 1. What is one application of PCA that helps in understanding the structure of high-dimensional data? A. Noise Production B. Data Duplication C. Data Analysis D. Data Visualization Answer: Data Visualization (D) PCA is used for creating 2D or 3D plots, allowing visualization of the patterns in high-dimensional data. 2. Which limitation of PCA refers to the challenge in understanding the principal components in relation to their original variables? A. Loss of Information B. Interpretability C. Dimensionality Reduction D. Non-linearity Answer: Interpretability (B) The interpretability of principal components can be less clear than that of the original variables. 3. Why is it necessary to standardize data before applying PCA? A. To enhance noise levels B. To eliminate dimensions C. To ensure uniform scaling of variables D. To improve interpretability Answer: To ensure uniform scaling of variables (C) PCA is sensitive to the scaling of the variables, making standardization essential before its application. 4. What is a potential issue when using PCA related to the nature of the relationships in the data? A. Assumption of Linearity B. Noise Reduction C. Feature Extraction D. High dimensionality Answer: Assumption of Linearity (A) PCA primarily works under the assumption that relationships in the data are linear. 5. What aspect of data does PCA struggle with due to its reliance on variance? A. Redundant Features B. Handling Missing Values C. Non-linear Relationships D. Bias in Data Answer: Non-linear Relationships (C) PCA is not capable of effectively handling complex relationships or non-gaussian distributions. 6. What is the primary objective of Principal Component Analysis (PCA)? A. To increase the number of variables in a dataset. B. To decrease the complexity of data without altering its original structure. C. To transform correlated variables into uncorrelated variables. D. To maximize the number of data points in a dataset. Answer: To transform correlated variables into uncorrelated variables. (C) The main goal of PCA is to change correlated variables into a smaller number of uncorrelated variables, known as principal components. 7. Which of the following steps is essential before conducting Principal Component Analysis? A. Visual inspection of data distribution. B. Elimination of outliers from the dataset. C. Normalization of the covariance matrix. D. Standardization of the data. Answer: Standardization of the data. (D) Standardizing the data ensures that each variable has a mean of zero and a variance of one, which is crucial for PCA. 8. What do eigenvalues in the context of PCA represent? A. The standard deviation of the data points. B. The variance explained by each principal component. C. The average of the dataset. D. The number of variables in the dataset. Answer: The variance explained by each principal component. (B) Eigenvalues reflect the amount of variance that each principal component captures in the data. 9. How are the principal components chosen in PCA? A. Randomly, regardless of their properties. B. By performing clustering analysis on the data. C. Based on their correlation with the original variables. D. By selecting the eigenvectors with the largest eigenvalues. Answer: By selecting the eigenvectors with the largest eigenvalues. (D) The top eigenvectors, corresponding to the largest eigenvalues, are selected as principal components to maximize variance. 10. What does it mean for principal components to be orthogonal? A. They are correlated despite their construction. B. They represent the same direction in the data. C. They have no effect on the variance of the data. D. There is no linear relationship between them. Answer: There is no linear relationship between them. (D) Orthogonality implies that principal components do not have any linear relationships, making them uncorrelated. 11. Why is standardization an important step in PCA? A. It prevents larger scale variables from dominating the analysis. B. It summarizes the data into single values. C. It maximizes the dataset size. D. It helps in maintaining the original scale of measurement. Answer: It prevents larger scale variables from dominating the analysis. (A) Standardization ensures that variables with larger scales do not disproportionately influence the PCA results. 12. In PCA, what is the role of the covariance matrix? A. It identifies outlier data points. B. It measures the total distance of data points from the mean. C. It calculates the average values for each variable. D. It captures the pairwise relationships among the variables. Answer: It captures the pairwise relationships among the variables. (D) The covariance matrix quantifies how much two variables change together, providing insights into their relationships. 13. What is obtained after projecting data onto principal component axes? A. The original data values. B. Covariance values of the original variables. C. Randomized values with no relation to the original data. D. Principal component scores. Answer: Principal component scores. (D) The projection onto the principal component axes results in principal component scores, which represent the data in a reduced dimension.